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On a hybrid data cloning method and its application in generalized linear mixed models

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Abstract

The data cloning method is a new computational tool for computing maximum likelihood estimates in complex statistical models such as mixed models. This method is synthesized with integrated nested Laplace approximation to compute maximum likelihood estimates efficiently via a fast implementation in generalized linear mixed models. Asymptotic behavior of the hybrid data cloning method is discussed. The performance of the proposed method is illustrated through a simulation study and real examples. It is shown that the proposed method performs well and rightly justifies the theory. Supplemental materials for this article are available online.

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References

  • Baghishani, H., Mohammadzadeh, M.: A data cloning algorithm for computing maximum likelihood estimates in spatial generalized linear mixed models. Comput. Stat. Data Anal. 55, 1748–1759 (2011)

    Article  Google Scholar 

  • Bellio, R., Varin, C.: A pairwise likelihood approach to generalized linear models with crossed random effects. Stat. Model. 5, 217–227 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Booth, J.G., Hobert, J.P., Jank, W.: A survey of Monte Carlo algorithms for maximizing the likelihood of a two-stage hierarchical model. Stat. Model. 1, 333–349 (2001)

    Article  MATH  Google Scholar 

  • Breslow, N.E., Clayton, D.G.: Approximate inference in generalized linear mixed models. J. Am. Stat. Assoc. 88, 9–25 (1993)

    Article  MATH  Google Scholar 

  • Crowder, M.J.: Beta-binomial ANOVA for proportions. Appl. Stat. 27, 24–37 (1978)

    Google Scholar 

  • Eidsvik, J., Martino, S., Rue, H.: Approximate Bayesian inference in spatial generalized linear mixed models. Scand. J. Stat. 36, 1–22 (2009)

    MathSciNet  MATH  Google Scholar 

  • Fong, Y., Rue, H., Wakefield, J.: Bayesian inference for generalized linear mixed models. Biostatistics 11, 397–412 (2010)

    Article  Google Scholar 

  • Hosseini, F., Eidsvik, J., Mohammadzadeh, M.: Approximate Bayesian inference in spatial generalized linear mixed models with skew normal latent variables. Comput. Stat. Data Anal. 55, 1791–1806 (2011)

    Article  Google Scholar 

  • Karim, M.R., Zeger, S.L.: Generalized linear models with random effects: Salamander mating revisited. Biometrics 48, 631–644 (1992)

    Article  Google Scholar 

  • Komarek, A., Lesaffre, E.: Generalized linear mixed model with a penalized Gaussian mixture as a random effects distribution. Comput. Stat. Data Anal. 52, 3441–3458 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Lele, S.R., Dennis, B., Lutscher, F.: Data cloning: easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods. Ecol. Lett. 10, 551–563 (2007)

    Article  Google Scholar 

  • McCullagh, P., Nelder, J.A.: Generalized Linear Models. Chapman and Hall, London (1989)

    MATH  Google Scholar 

  • McCulloch, C.E.: Maximum likelihood algorithms for generalized linear mixed models. J. Am. Stat. Assoc. 92, 162–170 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Ponciano, J.M., Taper, M.L., Dennis, B., Lele, S.R.: Hierarchical models in ecology: confidence intervals, hypothesis testing, and model selection using data cloning. Ecology 90, 356–362 (2009)

    Article  Google Scholar 

  • Rue, H., Held, L.: Gaussian Markov Random Fields: Theory and Applications. Chapman & Hall/CRC Press, Boca Raton/London (2005)

    Book  MATH  Google Scholar 

  • Rue, H., Martino, S.: Approximate Bayesian inference for hierarchical Gaussian Markov random fields models. J. Stat. Plan. Inference 137, 3177–3192 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Rue, H., Martino, S., Chopin, N.: Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J. R. Stat. Soc., Ser. B 71, 319–392 (2009)

    Article  MathSciNet  Google Scholar 

  • Thall, P.F., Vail, S.C.: Some covariance models for longitudinal count data with overdispersion. Biometrics 46, 657–671 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  • Weng, R.C., Tsai, W.C.: Asymptotic posterior normality for multiparameter problems. J. Stat. Plan. Inference 138, 4068–4080 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Hossein Baghishani.

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Baghishani, H., Rue, H. & Mohammadzadeh, M. On a hybrid data cloning method and its application in generalized linear mixed models. Stat Comput 22, 597–613 (2012). https://doi.org/10.1007/s11222-011-9254-z

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  • DOI: https://doi.org/10.1007/s11222-011-9254-z

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